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330 Answered Questions for the topic Calculus 2

Calculus 2


Suppose f(x) is a function with continous Derivatives...

Suppose f(x) is a function with continous Derivatives and.. f(8) = 4   f'(8)= 5   f''(8)=-4   f'''(8)= 1   a.) Write the Taylor Polynomial of degree 3 (first four terms) of f(x) centered at... more
Calculus 2 Calculus Integrals


How do I solve this Integral? (Pic attached in link)

I have been stuck on this integral for 3 hours. Here is what I have so far.. :
Calculus 2


How to prove that the limit lim_{(x,y)->(1,2)} (e^{y(x-1)}-1)/(1-x)(y+1) exists and equal to -2/3 ?

Prove that   
Calculus 2 Calculus Integration


Which limits do you use when finding arclength of a rose?

What is the arclength of r=6sin(3θ)? Given the formula Lpolar= ∫√[r^2+(dr/dθ)^2]dθ I can find the arc length using the r stated above and r'=18cos(3θ) Given that one petal is between θ of 0 and... more


how do I simplify these trig expressions?

cos-1(cos(47pi/12) arcsin(tan(-pi/6)) csc-1(cos(2017pi/2018)) cot(arcsin(1/2 csc(-11pi/4)))
Calculus 2


What Double Integral represents and its applications?

I want Correct answer
Calculus 2 Math Math Help


This was on my first Calc 2 quiz: $2\int_{-3}^{3}e^x^4dx$

I feel that there should be another x in the problem so that u sub works, or something, as it is I believe it is a partial gamma function or something, but I know we should not learn those until... more
Calculus 2 Fractions Integration


Fractions Equal??

Just wondering: Are these two quantities equal?(2/3)x^3 = 2x^(3)/3 ??Please be as detailed in your explanation as possible, perhaps proving your response. It is appreciated!
Calculus 2 Math Calculus


Consider the function f(x)=e^(3x)*g(x) , where g(0)=13 and g′(0)=−2 Find f′(0)

 This is for my homework I need an explanation of how to do this. please
Calculus 2


What is the formula for the sequence -3,5,-7,9,-11...

Find a formula for sn for n>1, for the sequence -3, 5, -7, 9, -11 ...
Calculus 2


Calculus II Magnitude and Direction of Vectors

I have worked this problem at least 8 different times and keep getting the same answer every single time. Could somebody please explain how to work this problem? Here is the problem: The magnitude... more
Calculus 2 Math Calculus


I'm having trouble with series.

Let f(x)= ∑∞n=0 (x^n)/(n!) Find f(0)= 1 f(1)= e f'(x)= f(x) f''(x)= f(x) Not exactly sure how we're supposed to go about finding those answers, or how to start.
Calculus 2


Sequence and bounds

I found that the limit of the sequence (1+22/n)^n is e^22. I'm told the sequence is bounded because the absolute value of an is < or = to e^22 for all positive integers.    I would like to... more
Calculus 2 Physics


How much a force will stretch a spring

Suppose that a spring has a natural length of 20 cm, and that 7 J of work is needed to stretch from a length of 30 cm to 50 cm. How far beyond its natural length will a force of 28 N keep the... more
Calculus 2 Calculus Power Series


Find the power series of (x^2)ln(3-x) using term by term differentiation/integration?

how would you find the power series representation of x2ln(3-x) using term by term differentiation or integration?
Calculus 2


a mouse farm starts with 3 mice, and two months later has 18 mice. Assume the population growth continues exponentially.

Find the function that models the population after t months. Find the population after 9 months. When will the population reach one million mice
Calculus 2 Math Limits


Determine whether the sequence converges or diverges. If it converges find the limit.

an=e(-1/sqrt(n)) Apparently in converges and the limit is 1 but I'm not really sure how to do this type of problem with a limit of ex   {n2e-n} Limit converges to 0? How?    
Calculus 2 Calculus Calculus 3


Consider the curve C given by the equation

Consider the curve C given by the equation: C · · · √ x + √ y = √ a, where a is a constant, a > 0. Let (x0, y0) with x0 > 0, y0 > 0, be a point on C. If (x1, 0) and (0, y1) are x and y... more
Calculus 2 Calculus Calculus 3


Given any Cartesian coordinates, (x,y), there are polar coodinates

Given any Cartesian coordinates, (x,y), there are polar coordinates (r,θ) with (-pie/2) < θ ≤ (pie/2). Find polar coordinates with (-pie/2) < θ ≤ (pie/2) for the following Cartesian... more
Calculus 2 Math Geometric Series


A ball drops from a height of 20 feet. Assume it goes on forever, find the total distance it travels.

A ball drops from a height of 20 feet. Each time it hits the ground, it bounces up 40 percents of the height it fall. Assume it goes on forever, find the total distance it travels.
Calculus 2 Calculus 3


Use substitution x=sin theta to evaluate integrate x^2/(1-x^2)^5/2

Full working out please
Calculus 2


Determine the minimum number of terms needed to approximate Tan-1(1.1) so that |S-Sn|<10^-6

I think that i need to use a maclaurin series, but i dont understand how to go about this, if anyway could help, i would appreciate.
Calculus 2 Calculus


how would i find the y = version of this expression?

i need to turn xy = yx into a y = version so that i can take its derivative. how would i go about this?
Calculus 2


how do you write an expression as a power of e?

For my homework i am to write 5^x^3 as a power of e. how do i go about doing this?
Calculus 2 Calculus


Calculate the Laplace Transform of the function f(t)=1

Calculate the Laplace Transform of the function f(t)=1
1 3 5 6 7 14

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